Shearforce and bending moment . Theory of structures . CVE 211

1. SHEAR FORCE AND BENDING MOMENT IN
BEAMS
BY
ENGR. (MRS) ADEBIYI A.Y
CVE 211

2. INTRODUCTION
 Beam is a structural member (Bar) resting on supports to carry vertical
loads. Generally, beams are placed horizontally. Whenever a horizontal
beam is loaded with vertical loads, sometimes it bends (i.e it deflects) due to
the action of the load.
 The bending however, is a function of
i. The amount and type of loads
ii. The type of beam
iii. The length of the beam
iv. The elasticity of the beam
The scientific way of studying the deflection or any other effect is to analyze
and draw the SHEAR FORCE and BENDING MOMENT DIAGRAMS of the
beam.

3. CLASSIFICATION OF BEAMS
I. Cantilever Beam: A beam
having its one end fixed or
built-in and the other end
free.
II. Simply Supported Beam: A
beam having its ends freely
resting on support.
III. Overhanging Beam: A beam
having one or both ends
extended over the supports.
IV. Rigidly Fixed or Built-in
Beam: A beam having its both
ends rigidly fixed or built-in to
the supporting walls or
columns.
V. Propped Beam: A beam
having a support at a suitable
point of a cantilever beam in
other to resist the deflection of
the beam.
VI. Continuous Beam: A beam
which rest on more than two
supports
Propped Beam
Cantilever
Overhanging
Fixed end

4. TYPE OF LOADS ON BEAMS ON BEAMS
I. Concentrated Load/ Point Load:
These loads are usually considered
to be acting at a point and are
denoted by Newton(N) or Kilo-
Newton(kN)
II. Uniformly Distributed
Load(UDL): It’s a type of load
which spread uniformly over the
entire length of the beam so that
each unit of length is loaded with
the same amount of load
III. Gradually Varying Load / Varying
Distributed Load(VDL): It’s a type
of load which spread uniformly
varying along the length of the
beam

5. TYPE OF SUPPORTS
There are three types of support
I. Roller Support: The roller supports has
only one reaction. It is unable to resists
the lateral loads. It resist only vertical
loads. The best example of roller support
is the roller skates. The roller skates
resist the vertical loads of the persons
standing on it.
I. Hinge Support: The pinned support has
two support reactions and these are
vertical and horizontal reactions. It allows
the structural member to rotate. The
pinned support is also known as hinge
support.
I. Fixed Support It is a support which is
capable of resisting all types of loads i.e.
horizontal, vertical as well as moments.
The fixed support is also called as rigid
support.
R=1
R=2
R=3

6. SHEAR FORCE AND BENDING MOMENT
Shear force (SF) : Shear force at the crossection of a beam may be defined as the algebraic
sum of all the forces taken either to the left or right side of the section.
Bending Moment (BM): Bending moment at any section of a beam may be defined as the
algebraic sum of all the moment of forces taken either to the left or right side of the section.
NOTE:An exception to this is a cantilever beam. Its calculation usually starts from the
free end
Sign Convention
Shear Force: Due to the shear force, one portion of the beam slide upward or downward with
respect to one another.
Bending Moment: The sign convention for bending moment can either be sagging (+ve
moment ) or hogging (-ve moment)

7. EQUATIONS OF EQUILIBRUM

8. SHEAR FORCE AND BENDING MOMENT DIAGRAMS
FOR VARIOUS BEAMS